We consider in this section the RTE with absorbing boundary, that is, the case where the input boundary intensity is null \(g\equiv 0\) . Non homogeneous boundary conditions follows from this case using classical arguments involving “lifting”, refer for example to the classical reference [1]}. In the case of absorbing boundary conditions, the natural domain of the operator \(\mathcal {L}:\mathcal {D}(\mathcal {L})\rightarrow L^{2}_{x,\theta }\)  is
\(\mathcal {D}(\mathcal {L})= H^{s}_{\mathcal {L}}\cap \big \lbrace  \gamma ^{-}(\cdot )=0 \big \rbrace \,.\) 
